Question 5 of 15, Step 1 of 1 Correct The following table gives the data for the hours students spent on homework and their grades on the first test. The equation of the regression line for this data is $\hat{y}=46.027+1.061 x$. This equation is appropriate for making predictions at the 0.01 level of significance. If a student spent 14 hours on their homework, make a prediction for their grade on the first test. Round your prediction to the nearest whole number. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{10}{|c|}{ Hours Spent on Homework and Test Grades } \\ \hline Hours Spent on Homework & 28 & 11 & 38 & 50 & 15 & 39 & 40 & 35 & 10 & 26 \\ \hline Grade on Test & 75 & 62 & 83 & 93 & 54 & 84 & 92 & 89 & 50 & 88 \\ \hline \end{tabular} Copy Data Answer How to enter your answer (opens in new window) Keypad Keyboard Shortc
Solution
Step 1 ：The question is asking to predict the grade of a student who spent 14 hours on their homework using the given regression line equation. The regression line equation is a linear equation in the form of \(y = mx + c\), where \(m\) is the slope of the line, \(x\) is the independent variable (in this case, hours spent on homework), and \(c\) is the y-intercept.
Step 2 ：Given that the slope \(m = 1.061\), the intercept \(c = 46.027\), and the student spent 14 hours on their homework, we substitute these values into the equation.
Step 3 ：The predicted grade is then calculated as \(46.027 + 1.061 \times 14\).
Step 4 ：Rounding this to the nearest whole number, we get the predicted grade as 61.
Step 5 ：So, the predicted grade for a student who spent 14 hours on their homework is \(\boxed{61}\).
